Since third-generation mobile communication services began, up till now, multimedia communication such as data communication and video communication has been gaining popularity. Consequently, data sizes are expected to increase even more in the future, and growing demands for higher data rates for mobile communication services are also anticipated.
Therefore, in ITU-R (International Telecommunication Union Radio Communication Sector), to realize high speed transmission of 1 Gbps in the downlink, the fourth-generation mobile communication system called IMT-Advanced is studied.
As error correcting codes to realize such high speed transmission, an LDPC (Low-Density Parity-Check) code attracts attentions (see Non-Patent Document 1). Use of an LDPC code as an error correcting code enables decoding processing to be parallelized, so that it is possible to make decoding processing faster than a turbo code whereby decoding processing needs to be performed serially and iteratively.
Further, a rate-compatible LDPC code is studied whereby a single encoder or single decoder can support a plurality of coding rates (Non-Patent Document 2).
On the other hand, when ARQ (Automatic Repeat Request) is applied to mobile communication, a radio communication apparatus on the data receiving side reports an error detecting result of received data, namely, ACK (acknowledgement) or NACK (negative acknowledgement) to a radio communication apparatus on the data transmitting side.
Here, as an error detecting method upon using an LDPC code as an error correcting code, there are cases where (1) an error detecting code such as a CRC (Cyclic Redundancy Check) code is used and where (2) a syndrome value is utilized. A syndrome value refers to a vector value generated by multiplying a parity check matrix for LDPC code and hard-decision value (decoded bit sequence) of received data, and is a parameter showing a degree of error of the received data. In error detecting utilizing syndrome values, when all the syndrome values are zero, the received data is determined not to have error and ACK is reported, and, when any syndrome value is not zero, the received data is determined to have error and NACK is reported.    Non-Patent Document 1: Low-Density Parity-Check (LDPC) Coded OFDM Systems—Coding/Decoding Over Time and Frequency Domains—, Hisashi FUTAKI and Tomoaki OHTSUKI, THE INSTITUTE OF ELECTRONICS, INFORMATION AND COMMUNICATION ENGINEERS, TECHNICAL REPORT OF IEICE, NS2001-91, RCS2001-92, pp. 79-84, 2001-07    Non-Patent Document 2: R1-051383, “Rate-compatible LDPC codes with low complexity & decoder”, Mitsubishi Electric Corporation, NTT DoCoMo, 3GPP TSG-RAN WG1 #43 Meeting, 2005/11